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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
*2307185002*
0580/12
MATHEMATICS
October/November 2010
Paper 1 (Core)
1 hour
Candidates answer on the Question Paper.
Additional Materials:
Electronic calculator
Mathematical tables (optional)
Geometrical instruments
Tracing paper (optional)
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
If working is needed for any question it must be shown below that question.
Electronic calculators should be used.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to
three significant figures. Give answers in degrees to one decimal place.
For π, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 56.
This document consists of 12 printed pages.
IB10 11_0580_12/3RP
© UCLES 2010
[Turn over
2
1
x°
For
Examiner's
Use
79°
NOT TO
SCALE
57°
The diagram shows a quadrilateral.
Work out the value of x.
Answer x =
2
[1]
Caroline changed £200 into New Zealand dollars (NZ$).
The exchange rate was £1 = NZ$2.56 .
How many New Zealand dollars did she receive?
Answer NZ$
© UCLES 2010
0580/12/O/N/10
[1]
3
3
Francis recorded a temperature of −4°C on Sunday.
By Monday it had gone down by 3°C.
For
Examiner's
Use
(a) Find the temperature on Monday.
Answer(a)
°C [1]
(b) On Tuesday the temperature was −1°C.
Find the change in temperature between Monday and Tuesday.
Answer(b)
4
°C
[1]
The distance from the Sun to the planet Saturn is 1 429 400 000 kilometres.
Write this distance in standard form, correct to 3 significant figures.
Answer
5
km [2]
A factory makes doors that are each 900 millimetres wide, correct to the nearest millimetre.
Complete the statement about the width, w millimetres, of each door.
Answer
© UCLES 2010
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YwI
[2]
[Turn over
4
6
For
Examiner's
Use
F
C
NOT TO
SCALE
4 cm
B
A
6 cm
E
15 cm
D
The triangles ABC and DEF are similar.
AB = 6 cm, BC = 4 cm and DE = 15 cm.
Calculate EF.
Answer EF =
7
cm
[2]
Maria puts $600 into a bank account for 3 years at a rate of 3.4% per year compound interest.
Calculate how much will be in the account at the end of the 3 years.
Answer $
© UCLES 2010
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[3]
5
8
(a) Factorise completely.
For
Examiner's
Use
8pq + 12pr
Answer(a)
[2]
(b) Use your answer to part (a) to make p the subject of the formula below.
s = 8pq + 12pr
Answer(b) p =
[1]
9
North
Q
NOT TO
SCALE
North
840 m
65°
P
The diagram shows a straight road PQ.
PQ = 840m and the bearing of Q from P is 065°.
(a) Work out the bearing of P from Q.
Answer(a)
[1]
4
of the distance from P to Q.
7
How far is he from Q?
(b) Calvin walks
Answer(b)
© UCLES 2010
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m
[2]
[Turn over
6
10 The heights of 43 children are measured to the nearest centimetre.
Braima draws a bar chart from this information.
For
Examiner's
Use
16
14
12
10
Frequency
8
6
4
2
0
120-129
130-139
140-149
150-159
160-169
170-179
180-189
Height (centimetres)
A child is chosen at random.
Write down, as a fraction, the probability that the child will be
(a) in the group 140 – 149 cm,
Answer(a)
[1]
Answer(b)
[1]
Answer(c)
[1]
(b) less than 160 cm,
(c) in the group 160 – 169 cm.
© UCLES 2010
0580/12/O/N/10
7
11
For
Examiner's
Use
C
NOT TO
SCALE
D
55°
O
A
x°
y°
B
The diagram shows a circle, centre O, with diameter BC.
AB is a tangent to the circle at B and angle BCD = 55°.
A straight line from A meets the circle at D and C.
Calculate the value of
(a) x,
Answer(a) x =
[2]
Answer(b) y =
[1]
Answer(a)(i) x =
[1]
Answer(a)(ii) x =
[1]
Answer(b)
[1]
(b) y.
12 (a) Write down the value of x when
x
(i) 5 ÷ 52 = 54,
(ii)
1
49
x
=7 .
(b) Write down the value of 3p0.
© UCLES 2010
0580/12/O/N/10
[Turn over
8
13 Dominic, Esther, Flora and Galena shared a pizza.
(a) Dominic ate
1
5
18
Show that
of the pizza and Esther ate
2
7
For
Examiner's
Use
of the pizza.
of the pizza remained.
35
Do not use your calculator and show all your working.
Answer (a)
[2]
2
of the pizza that remained.
3
Find the fraction of the pizza that was left for Galena.
(b) Flora ate
Answer(b)
[2]
14
9.6 × 7.8 − 0.53 × 86
4.95
(a) (i) Rewrite this calculation with each number written correct to 1 significant figure.
Answer(a)(i)
[1]
(ii) Work out the answer to your calculation in part(a)(i).
Do not use a calculator and show all your working.
Answer(a)(ii)
[2]
(b) Use your calculator to work out the correct answer to the original calculation.
Answer(b)
© UCLES 2010
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[1]
9
15 Some children took part in a sponsored swim to raise money for charity.
The scatter diagram shows the results for 10 of the children.
100
For
Examiner's
Use
D
90
A
80
J
70
60
C
Money
raised 50
($)
40
H
I
E
30
F
20
G
10
0
50
B
100
150
200
250
300
350
400
450
500
550
600
Distance (metres)
(a) (i) How much further did A swim than J ?
Answer(a)(i)
m
[1]
(ii) How much more money did D raise than F ?
Answer(a)(ii) $
[1]
(b) The results for 2 more children are given in the table below.
Child
Distance (m)
Money raised ($)
K
125
35
L
475
80
Plot the results for K and L on the scatter diagram.
[1]
(c) What type of correlation does the scatter diagram show?
Answer(c)
© UCLES 2010
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[1]
[Turn over
10
16 Flags A and B are shown on the grid.
For
Examiner's
Use
y
6
5
A
4
3
2
1
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
x
–1
–2
–3
–4
B
–5
–6
(a) Describe fully the single transformation which maps flag A onto flag B.
Answer(a)
[3]
 5
.
 − 3
(b) On the grid, draw the translation of flag A by the vector 
© UCLES 2010
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[2]
11
17
 3

 − 3
For
Examiner's
Use
 − 5

 0
AB = 
AC = 
(a) Calculate AB + 3 AC .
(b) Write down
Answer(a)






[2]
=






[1]
.
Answer(b)
(c) AC is drawn on the grid below.
C
A
(i) On the grid, draw AB .
[1]
(ii) Write down the obtuse angle between AB and AC .
Answer(c)(ii)
[1]
Question 18 is printed on the next page.
© UCLES 2010
0580/12/O/N/10
[Turn over
12
18
D
For
Examiner's
Use
C
NOT TO
SCALE
18 cm
A
B
The diagram shows a square ABCD.
The length of the diagonal AC is 18 cm.
(a) Calculate
(i) the length of the side of the square,
Answer(a)(i)
cm
[2]
Answer(a)(ii)
cm2
[2]
cm2
[2]
(ii) the area of the square.
(b) A, B, C and D lie on a circle with diameter AC.
Calculate the area of this circle.
Answer(b)
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2010
0580/12/O/N/10